files / problems / ramsey-r55 / compute / q2 / certs / degree_obstructions.json
{
"degree_window": [
18,
24
],
"excluded_cycle_types": [
"13^3 1^4",
"29^1 1^14",
"31^1 1^12",
"37^1 1^6",
"41^1 1^2"
],
"n": 43,
"note": "For each possible number of p-cycles in an order-p permutation, a fixed vertex has degree p*k+d, where k counts adjacent p-cycles and 0<=d<fixed. R(4,5)=25 forces every degree into [18,24]. This is only a necessary condition for cycle types not listed as excluded.",
"rows": [
{
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"fixed": 41,
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]
},
{
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]
},
{
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24
]
},
{
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]
},
{
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]
},
{
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]
},
{
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]
},
{
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]
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{
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]
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{
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]
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24
]
},
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]
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]
},
{
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]
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{
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]
},
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]
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]
},
{
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},
{
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]
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]
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]
},
{
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]
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23,
24
]
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]
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]
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]
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]
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{
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]
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{
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{
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{
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{
"cycle_type": "43^1 1^0",
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}
]
}